Mathematics
In the adjoining figure, a chord AB of a circle of radius 10 cm subtends a right angle at the centre O. Find the area of the sector OACB and of the major segment. Take π = 3.14.
![In the adjoining figure, a chord AB of a circle of radius 10 cm subtends a right angle at the centre O. Find the area of the sector OACB and of the major segment. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.](https://cdn1.knowledgeboat.com/img/mla9/q37-c16-ex-16-3-mensuration-ml-aggarwal-solutions-icse-class-9-572x632.png)
Mensuration
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Answer
Given,
Radius of the circle = 10 cm
Angle at the centre subtended by a chord AB = 90°.
We know that,
Area of sector OACB =
= 3.14 × 10 × 10 ×
=
= 78.5 cm2.
In right angle △OAB,
Area of △OAB = × OA × OB
= × 10 × 10
= 50 cm2.
Area of minor segment = Area of sector OACB – Area of △OAB
= 78.5 - 50
= 28.5 cm2.
Area of circle = πr2
= 3.14 × 10 × 10
= 314 cm2.
Area of major segment = Area of circle – Area of minor segment
= 314 - 28.5
= 285.5 cm2.
Hence, area of sector OACB = 78.5 cm2 and area of major segment = 285.5 cm2.
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